To be fair, Ferdinand mentioned to Benno that the Archduke going to eat with commoners was absolutely unprecedented (and Ferdinand was at first clearly pissed that the meeting was taking place there, he wanted Sylvester to just summon the merchant, as is proper), so it is definitely not on the "normal" side of things for nobles, at least if you follow high ranking etiquette.
When you go in the sticks, like in Illgner, then the nobles get closer to the commoners, as Brigitte said, but that's a big no-no in the capital city.
Ferdinand and Kartstedt only came because they needed to, Karstedt because he's Sylvester bodyguard, and Ferdinand because he needed to be there to stop Sylvester from going even more on a rampage. After seeing the place, and how it is mostly styled like a mednoble house, with attendants serving them like nobles, that likely helped change their minds on the status of the Italian Restaurant.
As for Freida, you're partly correct but partly wrong. Yes, Damuel's brother will only take her as a mistress, but that's because it was Freida's choice. She was first offered to become a true wife, and she refused that deal in order to stay with her family until her coming of age. Freida explains that to Myne in P1V3 I think? (not sure it is mentioned in the manga, so spoiler from the LN Part 1 just in case)